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• W1965874261 abstract "A rigorous mathematical foundation for the cluster-expansion method is presented. It is shown that the cluster basis developed by Sanchez et al. [Physica A 128, 334 (1984)] is a multidimensional discrete Fourier transform while the general formalism of Sanchez [Phys. Rev. B 48, 14013 (1993)] corresponds to a multidimensional discrete wavelet transform. For functions that depend nonlinearly on the concentration, it is shown that the cluster basis corresponding to a multidimensional discrete Fourier transform does not converge, as it is usually assumed, to a finite cluster expansion or to an Ising-type model representation of the energy of formation of alloys. The multidimensional wavelet transform, based on a variable basis cluster expansion, is shown to provide a satisfactory solution to the deficiencies of the discrete Fourier-transform approach. Several examples aimed at illustrating the main findings and conclusions of this work are given." @default.
• W1965874261 created "2016-06-24" @default.
• W1965874261 creator A5075834139 @default.
• W1965874261 date "2010-06-04" @default.
• W1965874261 modified "2023-10-11" @default.
• W1965874261 title "Cluster expansion and the configurational theory of alloys" @default.
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• W1965874261 doi "https://doi.org/10.1103/physrevb.81.224202" @default.
• W1965874261 hasPublicationYear "2010" @default.
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